I have bid on a few private auctions. While I agree that it could be a shill bidders paradise, I keep in mind what the item is worth to me.
I'm sure many times you have said, "This is my maximum bid" if you stick by this and you can't go wrong.
I would guess there might be several reasons a seller would like to keep the identities private. One reason might be the potential of someone viewing the auction to try to negotiate a private sale if they had the same item available.
Another reason might be the seller may have the same motive in mind if he has multiples of the item to sell.
There are also instances where friends will not bid against each other, protecting identities might benefit the seller.
Bear in mind as big as our chip collecting community is, by other hobby standards we are a small group. It is difficult to have an auction for a good quality chip and not recognize the majority of bidders by their e-bay "handle".

My main focus has been, what is the most I would pay for this item, and let it go at that